I read an online article recently about whether PJs were "the best of both worlds" or a "a compromise that's not as good as either". The writer thought the latter. About 80% of the people posting comments disagreed. It seems like a classic YMMV - probably depends on the bass, which pups it has, active or passive, and (of course) what sound you're looking for in the first place.
I have the Fender Aerodyne Jazz bass which is a PJ and I love it. I have the P volume max'ed and the J at around 20-25%. Sometimes I'll roll the J up a bit (but almost never past 50%), or down a bit, or off altogether, but the P tends to stay on full.
I'm a bit confused by the OP comment "I generally like basses with relatively simple controls" though. I mean, the Aero has two pups, a volume pot for each one, and single tone control. I don't think it can get much simpler.